Cher: I Admire Chaz's Courage

Cher is more supportive than ever to her son, Chaz, who legally changed his gender and name last year.

The iconic singer held a small screening of the upcoming documentary Becoming Chaz at her Malibu home over the weekend. "Cher and 10 of her and Chaz's friends stood up and cheered when it was over," a friend of Cher's tells PEOPLE.

The friend says Cher told her during the screening, "I admire my son Chaz's courage for sharing his personal journey. Most important to me is that he is very happy. That's what I care about the most. He has my love and support."

Chaz, who was born Chastity Bono to the famed singing duo, Sonny and Cher, started his female-to-male sex change March 2009, shortly after his 40th birthday. The documentary tells the story of his transformation from a woman to a man. It is scheduled to air on Oprah's OWN Network next week.

Bono came out as a lesbian at age 18, when he was studying at New York University. Sonny Bono, who died in a skiing accident in 1998, was accepting of his decision, but Cher had trouble with it. She told Vanity Fair that, "If I woke up tomorrow in a guy's body, I would just kick and scream and cry and [expletive] rob a bank, because I cannot see myself as anything but who I am – a girl," she says. "I would not take it as well as Chaz has. I couldn't imagine it."

In the interview, she called Chaz a smart girl before correcting herself and calling him a boy. "This is where I get into trouble. … I still don't remember to call her 'him.' "